Answer:
ans d
Step-by-step explanation:
5 percent of 30 is 1.5 so d
In the figure above, segment BC is 4 units long, segment CD is 8 units long, and segment DE is 6 units
long. What is the length of segment AC?
6 is the length of segment AC in right-angled triangle .
What is a right-angle triangle, exactly?
A right-angled triangle is a particular kind of triangle in which one of the angles is 90 degrees. The combined angles of the other two are 90 degrees.
Perpendicular and the triangle's base make up the sides that the right angle is formed from. The hypotenuse, or third side, is the longest of the three. It is also known as the hypotenuse.
let length of AC is x
BC + CD = AC + DE
4 + 8 = X + 6
12 = X + 6
X = 6
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2/25
two fractions
I need help please this is too hard and can you tell me the answer please
Two equivalent fractions to 2/25 are given as follows:
4/50 and 8/100.
What are equivalent fractions?A fraction is a numerical representation of the division of the two terms x and y, as follows:
Fraction = x/y.
The terms are classified as follows:
The top term x is the numerator of the fraction.The bottom term y is the denominator of the fraction.Two fractions are called equivalent when the ratio between their numerators and denominators is the same.
The fraction in this problem is defined as follows:
2/25.
To obtain an equivalent fraction, we multiply both the numerator and denominator by the same constant, hence:
Multiplying by 2: 2/25 = 4/50.Multiplying by 4: 2/25 = 8/100.Missing InformationThe problem asks for two equivalent fractions to 2/25.
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Mitch plays chess with his aunt every Friday.
He's won 12 matches and lost 3 matches.
What is the experimental probability that Mitch will win the next match?
Drag each object to show whether cost is proportional to area in the situation represented.
Since the points on this graph represent a relationship between x- and y-values, a statement about the relationship which is true include the following: A, it cannot be proportional because the straight line through the points does not go through the origin.
What is a proportional relationship?In Mathematics, the graph of any proportional relationship between two (2) variables is always characterized by a straight line with the data points starting from the origin (0, 0) and passes through other unique data points on the cartesian coordinate.
By critically observing the graph which shows a relationship between the x-values and y-values, we can logically deduce that it does not start from the origin (0, 0) and as such, it does not represent a proportional relationship.
In this context, we can reasonably infer and logically conclude that cost is not proportional to area in the situation represented by this graph.
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I need help fr it’s timed and I’m struggling frfr help
The equation of the line passing through the points (0, 3) and (-5, 0) is y = -3/5 x + 3
What is the equation of the line?The equation of a line in slope-intercept form is y = mx + b, where m is the slope of the line and b is the y-intercept.
Here,
To find the equation of the line passing through the points (0, 3) and (-5, 0), we can use the slope-intercept form and the slope formula:
m = (y2 - y1) / (x2 - x1) = (0 - 3) / (-5 - 0) = -3/5
where (x1, y1) = (0, 3) and (x2, y2) = (-5, 0) are the coordinates of the given points.
Now we can substitute the value of m and the coordinates of one of the points into the equation of the line to find the value of b:
y = mx + b
3 = (-3/5)*0 + b
b = 3
So the equation of the line passing through the points (0, 3) and (-5, 0) is:
y = -3/5 x + 3
We can also convert the equation to point-slope form as :
y - y1 = m(x - x1)
y - 3 = (-3/5)(x - 0)
y - 3 = -3/5 x
y = -3/5 x + 3
Hence, the equation of the line passing through the points (0, 3) and (-5, 0) is y = -3/5 x + 3
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A man crosses a distance of 48 meters while going round a quadrilateral field twice. What will be the cost of fencing the field at the cost $1.75 per meter?
A man crosses a distance of 48 meters while going round a quadrilateral field twice. For 24 m cost of fencing the field is $42.
What is perimeter?The circumference of an object is known as its perimeter. For instance, your home has a yard that is enclosed. The length of the fence is the perimeter. The length of your fence is 200 feet if the yard is 50 feet by 50 feet. P = length + breadth + length + breadth is the equation for a rectangle's perimeter. Add the lengths of the four corners of a rectangle to find its perimeter. You can quickly locate all four sides if you only know the width and height (two sides are each equal to the height and the other two sides are equal to the width). Add the outcomes after dividing the height and breadth by two.Perimeter of the field is the total lengths of its boundary = 48/2 m = 24 m
For 1 m, cost of fencing the field = $1.75
Therefore, for 24 m cost of fencing the field = $(1.75 × 24) = $42
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Find dy/dx of i)x, ii)xy, iii) y^2, iv) x^2y
Answer: i) dy/dx of x = 1
ii) dy/dx of xy = y
iii) dy/dx of y = 2y
iv) dy/dx of xy = 2xy
Step-by-step explanation:
58
n 8: Notes
potes
Name
2.
JuliAN A.
A plant's height is proportional to
the number of days since it was
purchased. On Day 6, it was 3 inches
tall.
1.
Add more points to the graph to
represent the plant's height on
other days.
Height of a Plant (in.)
1
5
(63)
5
10
Days Since Purchased
Should the origin, (0, 0), be included in this relationship?
Why or why not?
The height define how long the attribute is and the width specify about the breadth of the attributes.
What is height?Height is defined in mathematics as the vertical distance separating an object's top from its base. On occasion, it is referred to as "altitude". In coordinate geometry, an object's height is calculated along the y-axis and is referred to as height.height, altitude, elevation mean vertical distance either between the top and bottom of something or between a base and something above it. height refers to something measured vertically whether high or low.Height is measure of vertical distance, either vertical extent (how "tall" something or someone is) or vertical position (how "high" a point is). For example, "The height of that building is 50 m" or "The height of an airplane in-flight is about 10,000 m".Height is a common body measurement typically measured in feet (ft) + inches (in) in the United States and centimeters (cm) elsewhere. These are length measurements, so the SI unit would be meters. Keep in mind that x feet + y inches is commonly denoted as x' y“.
Given:
Arty's height is 63 inches.
Suppose Julian's height is x inches.
As Arty's height is 3 inches less than 1.5 times Julian's height.
⇒ 1.5x - 3 = 63
1.5x = 63 + 3
1.5x = 66
x = 44
Hence, the Julian's height is 44 inches.
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please help asap thanks . i’ll mark brainliest !!
Answer: 3
Step-by-step explanation: Whenever we have midsegment, the length of it is half of the base which is 30 so 5x =15.
Find -3p. p= (3 , 5 ) and q=(-2,10)
For p = (3, 5), the value of - 3p is (- 9, - 15).
What is Multiplication?To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.
We have to given that;
The values are,
⇒ p= (3, 5) and q = (-2, 10)
Now, We can find the value of - 3p as;
⇒ - 3 p
Substitute p = (3, 5) we get;
⇒ - 3 × (3, 5)
⇒ (3×- 3, - 3×5)
⇒ (- 9, - 15)
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The population of a town increased from 3600 in 2007 to 4700 in 2011. Find the absolute and relative (percent) increase.
1100 Absolute is a 30.55% increment relative percent
To find an Increment percentage in population we need the Number of increases in population.
4700- 3600 = 1100
That is absolutely increased number.
For relative increment, we need to find the Percentage -
Increment Percentage = (value / total value) * 100%so the population in 2007 was 3600
so percentage = 1100/3600*100
=> 30.55%
SO Relative increase = 30.55%
Here we can see that percent is the way to analyze the change, Increment/decrease in terms of 100 as it multiple the fractional changes in quantity by 100 to make it out of 100. So percentage simply means out of 100.
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Researchers routinely chose an alpha level of 0.05 for testing their hypotheses. What are some experiments for which you might want a lower alpha level (e.g., 0.01)? What are some situations you might accept a higher level (e.g., 0.1)?
Researchers frequently select a level of significance of 0.05. The reason for this is that if we chose a lower threshold of significance, we will have less room to reject the null hypothesis and so a higher likelihood of making a type 2 error.
On the other hand, if the degree of significance is higher, more type 1 errors are made, leading us to reject the hypothesis even though it is correct. Therefore, 0.05 is a balanced level that is neither significantly greater nor significantly smaller. The health care and nutrition-related industries are mostly included in some of the studies where we require a lower level of importance. This type of industry has a higher error rate, which causes more fatalities and negative side effects.
We can use a higher level of relevance in a variety of circumstances, such as the entertainment and marketing-related industries. The reason for this is that even if there are more potential for error, it won't harm the person; instead, it just affects the information, which we can assess using common sense.
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Compare the following decimals and choose either the greater than (>), less than (<), or equal to (=) sign as your answer. 187.567 _____ 187.68
Answer: 187.567 < 187.68
Step-by-step explanation:
0.6 is larger than 0.5 so 187.68 is bigger than 187.567
Two angles are complementary to each other. One angle measures 18°, and the other angle measures (8x − 28)°. Determine the value of x.
Answer:
Step-by-step explanation
since they are complementary their angles should add up to 90.
18+(8x-28)=90
you solve from there
add common values
8x-10+90
add 10 to both sides
8x=100
divide by 8
x=12.5
The answer is:
x = 12.5Work/explanation:
Since we're given both angles, we can set up an equation and find x.
The sum of two complementary angles is 90°.
Now, set up the equation:
[tex]\sf{8x-28+18=90}[/tex]
[tex]\sf{8x-10=90}[/tex]
Add 10 on each side
[tex]\sf{8x=100}[/tex]
Divide each side by 8
[tex]\sf{x=12.5}[/tex]
Hence, x = 12.5Write the equation of the line shown.
Answer:
y = 1/3x
Step-by-step explanation:
The equation is y = mx + b
m = the slope
b = y-intercept
The slope = rise/run
Let's pick 2 points (0,0) (3,1), we see the y increase by 1 and the x increase by 3, so the slope is
m = 1/3
The y-intercept is located at (0,0)
So, our equation is
y = 1/3x
Question 10 of 10
Which of the following graphs could represent a cubic function?
4.4?
B.
A.
○ A. Graph A
○ B. Graph B
○ c. Graph C
O D. Graph D
C.
D.
A graph which could represent a cubic function include the following: C. Graph C.
What is a function?In Mathematics, a function is a mathematical expression which can be used for defining and showing the relationship that exist between two or more variables in a data set.
What is a cubic function?In Mathematics, a cubic function is sometimes referred to as a cubic polynomial and it can be defined as a type of polynomial in which the degree of the highest term (coefficient or exponent) is equal to three (3).
In this context, we can reasonably infer and logically deduce that a graph that represents a cubic function is graph C because it models this polynomial y = x³.
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-Determine the eisen Value (s) and the corrosponding eigen vector(s) of
2 1 -1
3 2 -3
3 1 -2
The eigenvalues of the matrix are -1,1,3 and the corresponding eigenvectors are [-1,2,2], [1,-1,-1], [1,1,1] respectively.
How to determine the eigenvalues and the eigenvectorsThe matrix is given as
2 1 -1
3 2 -3
3 1 -2
To find the eigenvalues and eigenvectors of a matrix A, we need to solve the following equation:
Av = λv
where v is the eigenvector and λ is the eigenvalue.
So, we have
(2 1 -1) (x) = λ (x)
(3 2 -3) (y) (y)
(3 1 -2) (z) (z)
We can find the eigenvalues by solving the characteristic equation which is det(A-λI) = 0.
The characteristic equation for the above matrix is
(2-λ)((-λ-2)(-λ+1) - 2) - 3(1)(-λ+1) + 3(1)(-λ-2) = 0
Solving the above equation we get λ = -1,1,3
Now we can find the eigenvectors for each eigenvalue.
For λ = -1
(2 1 -1) (x) = -1 (x)
(3 2 -3) (y) (y)
(3 1 -2) (z) (z)
Solving the above equation we get x = -1, y = 2 and z = 2. So the eigenvector is [-1,2,2].
For λ = 1
(2 1 -1) (x) = 1 (x)
(3 2 -3) (y) (y)
(3 1 -2) (z) (z)
Solving the above equation we get x = 1, y = -1 and z = -1. So the eigenvector is [1,-1,-1].
For λ = 3
(2 1 -1) (x) = 3 (x)
(3 2 -3) (y) (y)
(3 1 -2) (z) (z)
Solving the above equation we get x = 1, y = 1 and z = 1. So the eigenvector is [1,1,1].
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Write a mixed number for t so that 2 3/4 X is more than 2 3/4
Answer: it will be improper
Step-by-step explanation:11/4
Answer:11/4
Step-by-step explanation:it is improper.
HELP PLEASE 80 POINTS!!! GOD BLESS WILL GIVE BRAINLIEST
PICTURE BELOW
Answer:
x ≥ -3 3/4
Step-by-step explanation:
-1/3x + 1/2 ≥ -3/4
1/3x ≥ -5/4
x ≥ -3 3/4
Victoria is a songwriter who collects royalties on her songs whenever they are played in a commercial or a movie. Victoria will earn $40 every time one of her songs is played in a commercial and she will earn $140 every time one of her songs is played in a movie. Victoria earned a total of $560 in royalties on 9 commercials and movies. Graphically solve a system of equations in order to determine the number of commercials,
x
,
x, and the number of movies,
y
,
y, on which Victoria's songs were played.
A graph of each function is shown in the image attached below.
The number of commercials (x) is equal to 7 commercials while the number of movies (y) is equal to 2 movies.
How to write and solve the system of equations graphically?In order to graphically solve the system of equations, we would write two (2) equations that models the situation by assigning variables to the number of commercials and number of movies respectively, and then translate the word problem into algebraic equation as follows:
Let the variable V represent the number of commercials.Let the variable y represent the number of movies.Since Victoria would earn $40 every time one of her songs is played in a commercial and $140 every time one of her songs is played in a movie, an equation which models it is;
40x + 140y = 560
Additionally, Victoria earned a total of $560 in royalties on 9 commercials and movies;
x + y = 9
Next, we would use an online graphing calculator to plot the above system of equations with a point of intersection at (7, 2) as shown in the image attached below.
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140,100,71.4, ,36.44 what is the missing number
The required missing number is 51.02
What is a geometric progression?Any progression in which the ratio of adjacent terms is fixed is a Geometric Progression. The general form of representation of a geometric sequence is a, ar, ar2, ar3, ar4, ar5, .....
Given here the numbers 140,100,71.4, ,36.44
clearly 140/100=100/71.4=1.4
Thus the given set of numbers form a geometric progression with common ratio 1.4
Therefore the complete set of numbers are 140,100,71.4,51.02,36.44
Hence, the required numbers is 51.02
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area of a trapezoid using decomposition pleas help wanted begs!
The area for the trapezoid is 35 square inches. Last option
How to solve for the trapezoidThe formula for the decomposition method of finding trapezoid is given as: ( x + y ) / h
The variables are given as
x = 3
y = 4
h = 5
we would have to fix the values into the formula in order to get the area of the trapezoid
Hence we would have
( 3 + 4) * 5
7 * 5
= 35 square units
Hence the area of the trapezoid by decomposition is given as 35 square units.
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The methods of statistics follow a process. Place the processes in the correct order:
Identify the research objective, Perform interference, Describe the data, Collect the data needed to Answer Research question
The order for the process of Statistcal Method will be Identify the research objective, Collect the data needed to Answer the Research question, Describe the data, and Perform Inference.
For any statistics method, we first must have an objective as to why are we conducting that research. Hence the first process has to be Identifying the research objective.
For any statistical method, samples need to be drawn to conduct statistic tests. This essentially requires data to work with. Hence, Collecting the data needed to Answer the Research question must be the next step.
After data is collected, numerous tests are possible to be performed on any set of data but to select the most appropriate statistic, we need to first understand the nature, range, and limitations of the data. Hence, the net step should be to describe the data.
The last step out of the available step would be to perform the inference since this is the only other step possible from the ones mentioned.
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The residents of a city voted on whether to raise property taxes. The ratio of yes votes to no votes was 7 to 4 . If there were 8657 total votes, how many yes votes were there?
Answer:
5509 yes votes
Step-by-step explanation:
We will start by adding together our ratio, so we know how many voters there were in a total ratio, so we can divide our total number of people by it, and then multiply it by the number of people who said yes (7 people).
Our ratio was 7:4, so adding those two numbers together gives us 11. Then, dividing 8657 by 11 gives us:
8657 / 11 = 787
Now, we will multiply 787 by 7, since that was the number of people who said yes:
787 * 7 = 5509
So, there were 5509 yes votes.
Hope this helped!
please need help asap!!!!!!!!!!!!!! please answer 28, and 29
The length of the midsegment of 28. is 17 units and 29. is 27 units.
What is midsegment?A line drawn by joining the midpoints of any two of the triangle's sides is known as the midsegment. All three sides of a triangle can be divided in half, with the midpoint being the point that is equally spaced from either vertex, regardless of whether the triangle is a right triangle, isosceles triangle, or sometimes an equilateral triangle.
If the slope and sides are same then we can cut the midsegment ad paste it such that it becomes an rectangle.
28. Now the length of the rectangle = n + 12 + n + 12 = 4n + 6 + 2n - 2
⇒ 2n + 24 = 6n +4
⇒ 20 = 4n
⇒ n = 20/4
⇒ n = 5
Length of midsegment = 5 + 12
= 17 units
29. Now the length of the rectangle = 2n+ 11 + 2n+ 11 = 5n - 2 + n + 8
⇒ 4n + 22 = 6n + 6
⇒ 16 = 2n
⇒ n = 16/2
⇒ n = 8
Length of midsegment = 2(8) + 11
= 27 units
Thus, he length of the midsegment of 28. is 17 units and 29. is 27 units.
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what number can divide 153 and 48. 50 points will.amrk as brainliest
Answer:
3
Step-by-step explanation:
3 can divide both 153 and 48
0.861 divided by 0.7
Answer:
1.23 calculator on cellphone do have that apps
Answer: 1.23
Step-by-step explanation: To find this answer, we need to move the decimal place. So, the 7 will move 1 place to the right of the 7, and then the decimal place will move to the right of the 8. So, now it should look like this:
[tex]\frac{08.61}{7}[/tex]
Then, divide using long division. You should get 1.23. To check, you can multiply 1.23 by 7, to get the dividend, 0.861. I hope this helped!
4.
11.2 in.
Sphere.!!! Helpppp.!!!
On solving the provided question we can say that the Volume of the sphere with radius 11.2 in is 5885 .
What is Sphere ?A sphere is a geometrical entity that resembles a two-dimensional circle in three dimensions. In three-dimensional space, a sphere is a collection of points that are all located at the same r-distance from a single point. The radius of the sphere is equal to r, and the provided point is its center.
characteristics of a sphere
The symmetry of a sphere is flawless.
A polyhedron is not a sphere.
Each point on the surface is equally spaced from the center.
There is no surface of centers on a sphere.
The mean curvature of a sphere is constant.
The breadth and circumference of a sphere are fixed.
Radius of sphere = 11.2 in
Volume = 4 pi r ^ 2 = 4 X 3.14 X 11.2 X 11.2 = 5885 .
Volume of the sphere with radius 11.2 in is 5885 .
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On solving the provided question we can say that the Volume of the sphere with radius 11.2 in is 5885 .
What is Sphere ?A sphere is a geometrical entity that resembles a two-dimensional circle in three dimensions. In three-dimensional space, a sphere is a collection of points that are all located at the same r-distance from a single point. The radius of the sphere is equal to r, and the provided point is its center.
characteristics of a sphere
The symmetry of a sphere is flawless.
A polyhedron is not a sphere.
Each point on the surface is equally spaced from the center.
There is no surface of centers on a sphere.
The mean curvature of a sphere is constant.
The breadth and circumference of a sphere are fixed.
Radius of sphere = 11.2 in
Volume = 4 pi r ^ 2 = 4 X 3.14 X 11.2 X 11.2 = 5885 .
Volume of the sphere with radius 11.2 in is 5885 .
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ASAP!!!! 100 POINTSS!!!!!
The function f(x) = 5x + 35 represents the distance in miles a drone flew.
The function g(x) = x + 7 represents the time the drone flew in hours.
Part A: Find f(3) and g(3). Show your work. (2 points)
Part B: Find f divided by g of 3. Show your work. (2 points)
Part C: What is the domain of f divided by g of x? (2 points)
The numeric values of each function at x = 3 are given as follows:
f(3) = 50.
g(3) = 10.
The division is given as follows: f(3)/g(3) = 5.
The space of f(x)/g(x) is given as all genuine values with the exception of x = - 7, as the function g(x), which is the denominator of the division, expects a worth of 0 at x = - 7.
To track down the numeric worth of a function or of articulation, we supplant each example of the variable in the function or in the articulation with the worth at which we need to track down the numeric worth.
Subsequently, the numeric values are found to supplant the solitary example of x by 3 in each function, as follows:
f(3) = 5(3) + 35 = 15 + 35 = 50.
g(3) = 3 + 7 = 10.
Subsequently, the division is given as follows:
(f/g)(3) = f(3)/g(3) = 50/10 = 5.
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a pair of dice are rolled. (a) what is the probability space s? (b) determine the probability of each of the following events: i. the sum of the rolls is even. ii. the first roll is equal to the second. iii. the first roll is larger than the second.
a)The probability Space, S = {(1,1) (1,2) (1,3) (1,4) (1,5) (1,6), (2, 1) (2, 2) (2,3) (2,5) (2,4),(2,6), (3,1) (3,2) ,(3,3), (3,4) (3,5)(3,6), (4,1) (4,2) (4,3) (4,4) (4,5) (4,6), (5,1) (5,2) (5,3) (5,4) (5,5) (5,6),(6,1) (6,2) (6,3) (6,4) (6,5) (6,4), (6,5),(6,6)}
b) i) Probability that the sum of the rolls is even, P(A) = 0.5
ii)Probability that first roll is equal to the second, P(B) 0.166
iii) Probability that the first roll is larger than the second, P(C) = 0.4166.
We have a pair of dice are rolled, then the Sample space is same as probability space.
a) The probability space , S is a non-empty set contains all possible outcomes. The probability space is written as
S = {(1,1) (1,2) (1,3) (1,4) (1,5) (1,6), (2, 1) (2, 2) (2,3) (2,5) (2,4),(2,6), (3,1) (3,2) ,(3,3), (3,4) (3,5)(3,6), (4,1) (4,2) (4,3) (4,4) (4,5) (4,6), (5,1) (5,2) (5,3) (5,4) (5,5) (5,6),(6,1) (6,2) (6,3) (6,4) (6,5) (6,4), (6,5),(6,6)}
b) Total possible outcomes from rolling = 36
Let us consider the events,
A : sum of the rolls is even
B : first roll is equal to the second
C : first roll is larger than the second.
Now, favourable outcomes for event A = 18
i) Probability (Sum is even), P( A) = 18/36
= 0.5
Favourable outcomes for event B = 6 = { (1,1),(2,2),(3,3),(4,4), (4,1) (4,2) (4,3), (5,5),(6,6)}
ii) So, Probability that first roll is equal to the second, P(B) = 6/36 = 0.166
Favourable outcomes for event C = 15 = { (2,1),(3,2),(3,1),(4,1),(5,1) (5,2) (5,3) (5,4),(6,1) (6,2) (6,3) (6,4) (6,5) (6,4), (6,5)}
iii) So, probability that the first roll is larger than the second, P(C) = 15/36
= 0.4166.
Hence, we get all required probabilities.
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The probability of P(Sum is even)=0.5, P(the first roll is equal to the second)=[tex]\frac{1}{6}[/tex], P(the first roll is larger than the second)=0.4167.
A pair of dice are rolled
Probability is a measure of the likelihood of an event to occur. Many events cannot be predicted with total certainty. We can predict only the chance of an event to occur.
The probability formula is defined as the possibility of an event to happen is equal to the ratio of the number of favourable outcomes and the total number of outcomes.a) Sample space,
[tex]$$\begin{aligned}S= & \left\{\begin{array}{l}(1,1)(1,2)(1,3)(1,4)(1,5)(1,6) \\(2,1)(2,2)(2,3)(2,4)(2,5)(2,6)\end{array}\right. \\& (3,1)(3,2)(3,3)(3,4)(3,5)(3,6) \\& (4,1)(4,2)(4,3)(4,4)(4,5)(4,6) \\& (5,1)(5,2)(5,3)(5,4)(5,5)(5,6) \\& (6,1)(6,2)(6,3)(6,4)(6,5)(6,2)\}\end{aligned}$$[/tex]
(b).
(i).The probability of each of the following events
Probability of event to happen
P(E) = Number of favourable outcomes/Total Number of outcomes⇒P(Sum is even)=[tex]\frac{18}{36} =\frac{1}{2}[/tex]=0.5
⇒P(Sum is even)=0.5
(ii). P(the first roll is equal to the second)=[tex]\frac{6}{36} =\frac{1}{6}[/tex]
⇒P(the first roll is equal to the second)=[tex]\frac{1}{6}[/tex]
(iii). P(the first roll is larger than the second)=[tex]\frac{15}{36}=0.4167[/tex]
⇒P(the first roll is larger than the second)=0.4167
Therefore, the P(Sum is even)=0.5, P(the first roll is equal to the second)=[tex]\frac{1}{6}[/tex], P(the first roll is larger than the second)=0.4167.
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